The present invention relates to an image display apparatus such as a head-mounted display (HMD) that uses a diffractive optical element.
A method for correcting chromatic aberrations in an optical system is known which uses a diffractive optical element having opposite chromatic aberration characteristics to those of a refractive surface (see U.S. Pat. No. 5,044,706). The diffractive optical element is also used for correction of aberrations other than chromatic aberrations, since it can have an effect as an aspheric surface by suitably setting its grating period.
When using such a diffractive optical element, it is desirable to design the diffractive optical element such that only diffracted light having a specific diffraction order (hereinafter referred to as “design diffraction order”) is generated from the diffractive optical element and that no diffracted light is generated in other diffraction orders.
In practice, however, when diffraction efficiency is determined in scalar approximation in, for example, a single-layer diffractive optical element, a diffraction efficiency of 100% for design diffraction order light can be achieved only when light of a specific wavelength (hereinafter referred to as “design wavelength”) enters the diffractive optical element at a specific incident angle. Thus, when the wavelength or incident angle of the entering light is offset from the design wavelength or the specific incident angle, the diffraction efficiency of the design diffraction order light decreases in increments of 10%. The decrease in the diffraction efficiency of the design diffraction order light increases diffracted light of other diffraction orders, which significantly deteriorates the performance of the optical system (see FIG. 1).
Meanwhile, Japanese Patent Laid-Open Nos. 9-127322 and 10-133149 disclose diffractive optical elements that achieve a high diffraction efficiency over a wide wavelength range. In these diffractive optical elements, plural diffraction grating portions formed of materials having mutually different dispersions are adjacently disposed. The diffraction order and grating height in the respective diffraction grating portions are adjusted, and thereby unnecessary light is reduced in a visible light wavelength range. Using materials with a large difference in dispersion for these diffraction grating portions makes it possible to achieve a scalar diffraction efficiency of near 100% over the entire visible light wavelength range.
Nevertheless, there are some cases where even the diffractive optical elements disclosed in Japanese Patent Laid-Open Nos. 9-127322 and 10-133149 cannot sufficiently reduce unnecessary light.
When the diffraction grating portion has a so-called blazed structure in which each of gratings in the diffraction grating portion has a grating surface 1 and a grating side surface 2 as shown in FIG. 2, light that has entered the grating side surface 2 at a certain angle is reflected or refracted at that grating side surface 2 and passes through the diffraction grating portion without being diffracted. Such non-diffracted light proceeds to a different direction from that of diffracted light of an original design diffraction order and becomes unnecessary light in the optical system.
To address this phenomenon, diffractive optical elements that reduce unnecessary light generated at grating side surfaces are disclosed in U.S. Pat. No. 5,801,889, and Japanese Patent Laid-Open Nos. 10-268115, 2003-294924, and 2005-292571.
In the diffractive optical element disclosed in U.S. Pat. No. 5,801,889, the radius of curvature of an enveloping surface of plural grating grooves and the angles of the grating side surfaces are optimized such that incident light hardly enters the grating side surfaces. In each diffractive optical element disclosed in Japanese Patent Laid-Open Nos. 10-268115, 2003-294924, and 2005-292571, the angle of incident light or emergent light is made equal to the angle of the grating side surface so as to reduce unnecessary light generated at the grating side surface.
However, even the diffractive optical elements disclosed in U.S. Pat. No. 5,801,889, and Japanese Patent Laid-Open Nos. 10-268115, 2003-294924, and 2005-292571 cannot sufficiently remove unnecessary light if the grating pitch is extremely small, e.g., several tens μm. In particular, in a diffractive optical element that combines plural diffraction grating portions, each grating has a height that is several to ten times higher than that of a single-layer diffractive optical element. Thus, the ratio of grating height relative to the grating pitch is larger. This indicates that the ratio of light rays impinging on the grating side surfaces relative to normally diffracted light rays increases.
When considering a case in which light rays enter a diffractive optical element having a shape shown in FIG. 3A, the diagram on the left side in FIG. 3A shows a central portion (portion around an optical axis) of the diffractive optical element, and the diagram on the right side shows a peripheral portion of this diffractive optical element. For the sake of simplicity, an enveloping surface 3 passing through apexes of plural gratings (grating tips) is indicated as a plane perpendicular to the optical axis, while the grating side surfaces 2 are indicated as planes parallel to the optical axis.
When the light rays enter this diffractive optical element parallel to the optical axis, they hardly impinge on the grating side surfaces 2, and a high diffraction efficiency is achieved in the design diffraction order.
On the other hand, when the light rays enter at a certain incident angle relative to the optical axis, the ratio of light rays entering the grating side surfaces 2 instead of the grating surfaces 1 increases as the incident angle increases. In this case, the ratio of the light rays impinging on the grating side surfaces 2 can be decreased by inclining the grating side surfaces 2 at an angle equal to the incident angle of the light rays as shown in FIG. 3B.
FIG. 4 shows a two-layer (multilayer) diffractive optical element having two diffraction grating portions with different dispersions which are facingly disposed with an air layer (gap) interposed therebetween in order to achieve a high diffraction efficiency over a wide wavelength range. A design diffraction order of the diffractive optical element in FIG. 4 is represented as M, and an entrance side diffraction grating portion is referred to as a first diffraction grating portion, while a diffraction side (emergent side) diffraction grating portion is referred to as a second diffraction grating portion. The first diffraction grating portion has a positive optical power, while the second diffraction grating portion has a negative optical power. Refractive indexes of an entrance side medium of the first diffraction grating portion and a diffraction side medium of the second diffraction grating portion are designated by n1 and n2, respectively.
An incident angle on the first diffraction grating portion is designated by θ1, while a diffraction angle in the design diffraction order by the first diffraction grating portion is designated by θ2 as shown in FIG. 5A. θ2 is also the incident angle on the second diffraction grating portion. A diffraction angle in the design diffraction order by the second diffraction grating portion is designated by θ3. Since the design diffraction order of the entire diffractive optical element including these two diffraction grating portions is an M-th order, the relationship between θ1 and θ3 is expressed as follows:θ3(k)=sin−1 [{n1·sin θ1(k)−M·λ/P(k)}/n2]
where k represents a number of each grating when the number of an innermost grating is 1, P represents a grating pitch of a k-th grating (grating pitch between the k-th grating and a (k−1)-th grating), and λ represents a design wavelength.
In order to achieve a high diffraction efficiency over a wide wavelength range, an optimal diffraction order in the first and second diffraction grating portions needs to be respectively determined. This will in turn determine a grating height in each diffraction grating portion, as well as θ2. When M is a fixed value, the respective design diffraction orders designated by m1 and m2 in the first and second diffraction grating portions must satisfy the following condition:M=m1+m2.
The incident angle θ2 on the second diffraction grating portion depends on the design diffraction orders of the respective diffraction grating portions. The relationships between θ1, θ2, and θ3 will be either of the following depending on the value of θ2, as shown in FIG. 5A and FIG. 6A:θ1≧θ2, θ2≦θ3  (11) orθ1≦θ2, θ2≧θ3  (12).
If the relationship of the expression (11) arises, as shown in FIG. 5B, light rays 101 and 201 entering grating surfaces 11 and 21 of the first diffraction grating portion at an incident angle of θ1 are diffracted at the first diffraction grating portion and proceed in a direction of θ2. In this case, if a grating side surface 13 of the first diffraction grating portion is inclined at an angle equal to the incident angle θ1, the light ray 101 that has entered near a grating groove of the grating surface 11 proceeds in a direction away from the grating side surface 13 and does not impinge thereon.
The light ray 201 that has entered near a grating groove of a grating surface 21 proceeds parallel to the grating side surface 13 and is correctly diffracted without impinging on the grating side surface 13. In this case, unnecessary light generated at the grating side surface 13 of the first diffraction grating portion is reduced.
On the other hand, if a grating side surface 14 of the second diffraction grating portion is inclined at an angle equal to the incident angle θ2, the light ray 102 that has entered near a grating groove of the grating surface 12 at an incident angle of θ2 is diffracted at a diffraction angle of θ3 to proceed towards the grating side surface 14 and impinges thereon. The light ray 202 that has entered near a grating groove of a grating surface 22 proceeds parallel to the grating side surface 14 and is correctly diffracted without impinging on the grating side surface 14.
If the relationship of the expression (12) arises, light rays impinging on the grating side surface 14 in the second diffraction grating portion are reduced, as shown in FIG. 6B. However, in the first diffraction grating portion, the light ray 101 that has entered near the grating groove of the grating surface 11 at the incident angle of θ1 is diffracted at the diffraction angle of θ2 to proceed towards the grating side surface 13 and impinges thereon.
These problems arise when the diffraction angle is larger than the incident angle. If the inclination angle of the grating side surface is made equal to the diffraction angle, but not equal to the incident angle so that the diffracted light ray does not proceed towards the grating side surface, then the grating side surface will be parallel to the diffracted light ray so that the diffracted light ray impinging on the grating side surface can be reduced. However, in this case, a light ray before being diffracted impinges on the grating side surface 13 as shown in FIG. 7, and therefore unnecessary light cannot be sufficiently removed.
When the grating pitch P is sufficiently large as compared to the grating height d, for example, if P=200 μm and d=10 μm, then a ratio d/P is as small as 0.05, which is allowable, since this means that a proportion (intensity) of unnecessary light relative to the light correctly diffracted in the direction of the design diffraction order at the grating surface is made small. However, if P=20 μm and d=8 μm, for example, then the ratio d/P is 0.4, in which case the proportion of the unnecessary light reaches a non-negligible level.